What is the value of k in the function f(x) = (2-k)/(5x+k) if its graph passes through the point (3, -2/19)
A. -19/2
B. 4
C. -10
D. No such k exists
I think its D, but I am not sure. Please help quickly.
This means that for x = 3, f(x) = -2/19
So, (2-k)/(5x+k) = -2/19
(2-k)/(15+k) = -2/19
38 - 19k = -30 -2k
68 = 17k
k = 68/17 = 4
To determine the value of k in the function f(x) = (2-k)/(5x+k), we can substitute the given point (3, -2/19) into the equation and solve for k.
Substituting x = 3 and f(x) = -2/19, we get:
-2/19 = (2-k)/(5(3)+k)
To solve for k, we can cross-multiply:
-2(5(3)+k) = (2-k)(19)
-30 - 2k = 38 - 19k
Now, simplify the equation:
-2k + 19k = 38 + 30
17k = 68
k = 68/17
k = 4
Therefore, the value of k is 4. The correct answer is option B.
To find the value of k in the function f(x) = (2 - k)/(5x + k) when its graph passes through the point (3, -2/19), we can substitute the x and f(x) values into the equation and solve for k.
Substituting x = 3 and f(x) = -2/19 into the equation, we get:
-2/19 = (2 - k)/(5(3) + k)
To simplify the expression, let's first distribute 5 to (3 + k):
-2/19 = (2 - k)/(15 + 5k)
Next, let's cross-multiply:
-2(15 + 5k) = (2 - k)(19)
Simplifying further:
-30 - 10k = 38 - 19k
Now, let's solve for k:
-19k + 10k = 38 + 30
-9k = 68
Dividing both sides by -9:
k = -68/9
Therefore, the value of k is -68/9.
None of the options A, B, or C match this value of k, so the correct answer is D.